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Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.

8 votes

Quantum group as (relative) Drinfeld double?

Yes! It is indeed, to get the quantum group $\mathcal{U}_q(\mathfrak{g})$, you have to... start with a groupring $\mathcal{U}^0(\mathfrak{g})=\mathbb{k}[\mathbb{Z}^n]=\langle K_1,\ldots K_n\rangle_{ …
Simon Lentner's user avatar
0 votes

$q$-Deforming Woronowicz's Leibniz Rule

At least the Drinfel'd-Jimbo quantum groups (dual to the coordinate rings) have a structure, that is usually explored by using so-called skew-derivations satisfying exactly the rule you name (see e.g. …
Simon Lentner's user avatar
3 votes

Non-Drinfeld–Jimbo deformations and finite quantum groups

Much depending on what you want to do with it.... ;-) There is a duality between coordinate algebras to the Drinfel'd-Jimbo $U_q(\mathfrak{g})$ (you're title suggests you're interested rather in the …
Simon Lentner's user avatar
3 votes

What is $\left[ \begin{array}{c} K_i;0\\ \ell\\ \end{array} \right] _{\varepsilon _i}$ in th...

You are correct and your observation is precisely the point. It is all about choices. You define the K-symbol as an element in the quantum group over $\mathbb{Q}(q)$. At a later point you more or less …
Simon Lentner's user avatar